Question:
A coin is tossed three times. If X denotes the absolute difference between the number of heads and the number of tails then P(X = 1) =
A coin is tossed three times. If X denotes the absolute difference between the number of heads and the number of tails then P(X = 1) =
Updated On: Sep 3, 2024
- $\frac{1}{2}$
- $\frac{2}{3}$
- $\frac{1}{6}$
- $\frac{3}{4}$
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The Correct Option is D
Solution and Explanation
Given, A coin is tossed three times
and $X=$ absolute difference between the number of heads and number of tails.
Now, $X=1$ when exactly two head or two tail comes
$\therefore P(X=1)=\frac{3}{8}+\frac{3}{8}=\frac{6}{8}=\frac{3}{4} $
$ [\because $ probability of exacty two head $ =\frac{3}{8} $,
and probability of exactly two tails $=\frac{3}{8} ]$
and $X=$ absolute difference between the number of heads and number of tails.
Now, $X=1$ when exactly two head or two tail comes
$\therefore P(X=1)=\frac{3}{8}+\frac{3}{8}=\frac{6}{8}=\frac{3}{4} $
$ [\because $ probability of exacty two head $ =\frac{3}{8} $,
and probability of exactly two tails $=\frac{3}{8} ]$
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Concepts Used:
Event
A probability event can be defined as a set of outcomes of an experiment. In other words, an event in probability is the subset of the respective sample space. The likelihood of occurrence of an event is known as probability. The probability of occurrence of any event lies between 0 and 1.
Thus, an event is a subset of the sample space, i.e., E is a subset of S.
There could be a lot of events associated with a given sample space. For any event to occur, the outcome of the experiment must be an element of the set of event E.
Probability of Occurrence of an Event
P(E) = Number of Favourable Outcomes/ Total Number of Outcomes
Types of Events in Probability:
Some of the important probability events are:
- Impossible and Sure Events
- Simple Events
- Compound Events
- Independent and Dependent Events
- Mutually Exclusive Events
- Exhaustive Events
- Complementary Events
- Events Associated with “OR”
- Events Associated with “AND”
- Event E1 but not E2